Bayesian stochastic search for VAR model restrictions

Abstract

We propose a Bayesian stochastic search approach to selecting restrictions for Vector Autoregressive (VAR) models. For this purpose, we develop a Markov Chain Monte Carlo (MCMC) algorithm that visits high posterior probability restrictions on the elements of both the VAR regression coefficients and the error variance matrix. Numerical simulations show that stochastic search based on this algorithm can be effective at both selecting a satisfactory model and improving forecasting performance. To illustrate the potential of our approach, we apply our stochastic search to VAR modelling of inflation transmission from Producer Price Index (PPI) components to the Consumer Price Index (CPI).

Bayesian Analysis of Latent Threshold Dynamic Models

“…, t. Much progress has been made in recent years in the general area of Bayesian sparsity modeling: developing model structures via hierarchical priors that are able to induce shrinkage to zero of subsets of parameters. The standard use of sparsity priors for regression model uncertainty and variable selection McCulloch 1993, 1997;Clyde and George 2004) has become widespread in areas including sparse factor analysis Carvalho et al 2008;Yoshida and West 2010), graphical modeling (Jones et al 2005), and traditional time series models (e.g., George et al 2008;Chen et al 2011). In the context of time series analysis, these general strategies have been usefully applied to induce "global" shrinkage to zero of parameter subsets, zeroing out regression coefficients in a time series model for all time (Carvalho and West 2007;George et al 2008;Korobilis 2012;Wang 2010).…”

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“…The first approach uses stochastic search variable selection (SSVS) priors put forward by George and McCulloch (1993) and George and McCulloch (1997), which have been widely applied especially in the time-series literature (see George et al 2008 andKoop andKorobilis 2010). SSVS priors rely on a mixture of normal priors, where the choice of the prior hyperparameters may have severe effects on posterior inference.…”